Elementary and Advanced Linear and Multilinear Algebra for Physics
Instructors: Univ.-Prof. Dr. Nikolaos PapadopoulosCourse No.: 08.128.7031
Course Type: Vorlesung
Requirements / organisational issues
A certain familiarity with solving systems of linear equations. Therefore, the lecture is suitable for any semester in both the Bachelor's and Master's programs.The lecture lasts 2 hours, followed by one hour for questions, discussions, and exercises as needed
Recommended reading list
N. Johnston: Introduction to Linear and Matrix Algebra, Springer, 2021;N.A. Papadopoulos, F. Scheck: Linear Algebra for Physics, SpringerNature, ISBN 978-3-031-64907-3. https://www.amazon.de/Linear-Algebra-Physics-Nikolaos-Papadopoulos/dp/3031649079 oder https://link.springer.com/book/10.1007/978-3-031-64908-0
Contents
A. On the content of the elementary part of the lecture:- An informal introduction to the concepts and notation of scalars, vectors, covectors, columns, rows, matrices. On matrix duality and the four aspects of matrix multiplication.
- Theory of abstract vector spaces, the role of bases for the representation of abstract vectors, and the role of indices.
- Theory of linear transformations and the role of bases for representing linear transformations through matrices. Properties of linear transformations. The fundamental theorem of linear algebra.
- Abstract Euclidean vector spaces.
- Elementary tensor calculus.
B. Advanced part of the lecture, as agreed upon with the participants.
Additional information
Important mathematicians, such as R. Bott, who have made significant contributions to physics, emphasize that 80% of mathematics is linear algebra. However, its importance is generally not adequately acknowledged in the study of physics. The goal of this lecture is to impart mastery of linear algebra and tensor calculus.Dates
| Date (Day of the week) | Time | Location |
|---|---|---|
| 11/04/2024 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 11/11/2024 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 11/18/2024 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 11/25/2024 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 12/02/2024 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 12/09/2024 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 12/16/2024 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 01/06/2025 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 01/13/2025 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 01/20/2025 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 01/27/2025 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |
| 02/03/2025 (Monday) | 16:15 - 18:45 | 01 231 Seminarraum E 2413 - Neubau Physik/Mathematik |